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Autos = Self
Bios = Life
Graphy=Writing
An autobiography is the author's retelling of their life. This is written in first person and the author is the main character.
N
Number theory:
types of numbers
divisibility rules
factors-multiples
example: 10 is divisible by 5 because 2 x 5 = 10
Divisibility Rules
Ending
Sum of the Digits
Last Digits
By 6
Prime Numbers: only two factors ( one and itself)
Add both your personal and professional accomplishments.
1) If a number is not divisible by 5, can it be divisible by 10?
No, because it may have a zero at the end.
2) If a number is not divisible by 10, can it be divisible by 5?
Yes, because the number may end in 5.
3) Can two numbers have a GCM?
No, because numbers are infinite.
4) Mary says that her factor tree for 72 begins with 3 and 24 so her prime factors will be different than Tom's because he starts with 8 and 9. What do you say to Mary?
Her method still works because she started with the greatest factor that will just need to be broken down or simplified.
5) The radio station gave away a discount coupon for every 12th and 13th caller. Every 12th caller received a free concert ticket. Which caller was first to get both a coupon and a concert ticket?
LCM: (12,13)
12: 12, 24,36,48,60,72
13:13,26,39,52,65,78
20:20,40,60,80
Answer: 60th caller
Prime Factorization
the fingerprint or DNA of every composite number. always the same
GCF and LCF
25: 1, 5, 25
100: 1, 2, 4, 5, 20, 25, 30, 36
List Method
24: 1,2,3,4,6,8,12,24
36: 1,2,3,4,6,9,12,18,36
Prime Factorization Method
24: 2 x 2 x 2 x3
36: 2 x 2 x 3 x 3
2 x 2 x 3 = 12
Add the things you like and make you a happy person!
Meanings
example: 3 divided by 5 = 3/5
Models
Ratio
20 students
12 girls
8 boys
example: 12/20 girls to the whole ratio
8/20 boys to a whole ratio
Sets (groups of things)
3/3 = 1 and 4/4 = 1
denominator and numerator are the same meaning its one whole.
Fractional parts are equivalent parts.
Example: 25/100 divided by 5 to both parts = 1/4
If there is something that you definitely don't like, add it here!
1) If 1/3 cup of sugar is needed to make two loaves of bread, how many cups of sugar are needed for 3 loaves?
*multiple diagrams divided into 6 equal parts to represent the amount of serving
It will take 2 1/6 of sugar
2) When the LCD is used in adding or subtracting fractions, is the result always a fraction in its simplest form? Explain.
Even though its the LCF, it doesn't mean it's simplified. LCF is still important because you are dealing with smaller numbers and are less likely to make a mistake.
1/2 + 1/6 = 4/6
1) A set of marbles can be divided into equal shares among 2,3,4,5 or 6 children w/ no marbles left over. What is the least number of marbles this set could have?
2: .... (2x30)
3: .... (3x20)
4: .....( 4x15)
5: .....(5x12)
6: .......(6x10)
Answer 60
2) Mary spent 2/3 of her money. She lost 2/3 of the remaining amount then she had $8 left. How much money did she start with?
*diagram split up into 9 equal parts representing the given values
9 x $8 =$72
1/4 + 2/4 = 3/4
Adding fractions with the same common denominator.
1/2 + 1/6
3/6 + 1/6 = 4/6
Even though its LCF, doesn't mean its simplified.
LCF is important because you are dealing with smaller numbers, less likely to error.
7/6 improper fraction = 1 1/6 which is a mixed number
Multiplication
1/2 of 1/2 is 1/2 x 1/2 which is 1/4
1/2 of 1/4 is 1/2 x 1/4 which is 1/8
The product gets smaller because you are losing a part of a part.
Division
2/3 divided by 4/5
2/3 x 5/4 (the reciprocal)
6 divided by 3
means how many times does 6 go into 3?
Add your vision for your future! You can choose to add your short term goal or long term goal!
1) *three diagrams divided into 4 equal parts
3/4 + 3/4 = 1 1/2
2/4 + 6/4 = 8/4 = 2
2) *pie graph divided into 8 equal parts
1/2 of 3/4
3/4 = 6/8 = 3/8
3) *4 stars = 2/7
2 stars = 1/7
14 stars are a whole
Did in-class examples representing math problems of taking part of a whole and taking part of a part.
Went over Exam #2 study guide
$111.11 = the decimal place can be represented with 1/10 and 1/100.
7 dimes is $0.70 and could also be 70%.
We practiced placing decimal numbers from smallest to greatest.
Rounding
round to the nearest 10's
37 : 40
0.7 : 1
0.37 : 0.40
pi 3.14 is an irrational number.
1) Using + for a positive and - for negative.
a) 4 - (-2) =+6
drew a picture representing the chips
b) 9+ (-2) = +7
drew a picture demonstrating a zero-pair
2) Write and solve using equations.
a) -17 + 10 = -7
b) -10 + +8 = -2
c) -4 x +3 =- 12
1) Change the following fractions to terminating or repeating decimals.
7/8 = 0.875
5/3 = 1.66 repeating
2) Express the following fractions as a decimal and a percent.
5/6 = 0.83 =83%
5/9 = 56%
3)
a) 24 is what percent of 180?
24 = n x 180
n=13%
b) 30% of what number is 21?
0.30 x n = 21
n= 70
a) 8 is what percent of 22?
8= n x 22
n= 8/22
b) 8% of 22 is what number?
0.08 x 22 = n
n=1.76
c) 8% of what number is 22?
0.08 x n = 22
n= 275
We did other practice problems following the same method.
1) A student takes a test w/ 45 questions and gets 37 questions right. What is their percentage on the test?
45 divided by 37 is 82%
We practiced many in-class problems relating to what percentage of a given amount.
Add the institutes where you got your degrees.
1) American Standard (last step)
2) European/Mexican (R-L)
8 from 16 is the same as 9 from 17.
3) Reverse Indian (L-R)
Starting from the hundreds and decreasing values if you need to borrow.
4) Left to Right
approaching the problem left to right starting with the hundreds place. this requires you to subtract the problems using full values with zero representing what place.
5) Expanded Notation
breaking down the problem by separating it by hundreds, tens, and ones and adding it by grouping the values.
6) Integer Subtraction
allows you to not borrow numbers but instead write the number as a negative if necessary.
1) American Standard (last step)
2) Partial Sums
using lines to correspond the the place value of the ones, tens, and hundreds.
3) Partial Sums w/ Place Value
similar to partial sums except you are writing in zero values.
4) Left to Right
approaching the problem left to right starting with the hundreds place.
5) Expanded Notation
breaking down the problem by separating it by hundreds, tens, and ones and adding it by grouping the values.
6) Lattice
using a structure to demonstrate the ones and tens values.
What and who made you who you are today?
8/2 : division or fraction bar
quotient, divisor, and dividend
the rinculum
We practiced the Standard Algorithm of division using long division.
Then we practiced a different long division method where it demonstrated place value.
Array: 3x2 means 3 groups of 2
Identity Property: ax1=a
Zero Property of mult: ax0=0
Commutative Property: axb=bxa
Associative Property: (axb)xc=ax(bxc)
Distributive Property: ax(b+c)=(axb)+(axc)
When I multiply the number by each of the parts
Subtraction (the difference)
meaning:
It's an addition problem, so subtraction would confuse a student as to why you are losing an object.
Comparison doesn't add or subtract
Addition (put together/join)
1) Identity Property: a+0=a
when I add zero to any number the property doesn't change.
2) Commutative Property (order): a+b=b+a
3) Associative Property (grouping): (a+b)+c=a(b+c)
Add information about your family. Usually, the mother's maiden name is written.
Additionally, you can add their age.
1. Write each of these numbers:
a) 29 in base 3= 1002 3
b) 69 in base 2= 1000101 2
c) 115 in base 5= 430 5
2. How do you know there is an error in each statement?
a) 10=243 and b) 13 3/4=25.34
You can't have a number bigger than the base
1. Give the Base-10 numeral for each given number. Use expanded notation to explain your answer:
a) 41.58= (4x8 1) + 1x8 0) +(5x1/8)
33 5/8
b) 13415= (1x5 3)+(3x5 2) +(4x5 1)+ (1x5 0)
221
2. Write the number 12 in each given base:
a) Base 9 =13 9
b) Base 8= 14 8
c) Base 7= 15 7
The number system we use in our schools and society is the Base-10 system. There is a consistent one-to-ten relationship between the digits of any number in the Base-10 system.
375
3-hundreds
7-tens
5-ones
0.35 is an example of parts of a whole
the decimal represents what percent of the unit applied.
Expanded Notation
375= 300+70+5
=(3x100)+(7x10)+(5x1)
=(3x102)+(7x101)+(5x100)
723=700+20+3
723=(7x100)+(2x10)+(3x1)
723=(7x10^2)+(2x10^1)+(3x10^0)
Base 5: 0,1,2,3,4, 105, 115 , 125 ,135 ,145 ,155
23.14
•A tenth of a unit is a tenth
•A tenth of a tenth is a hundredth
•A tenth of a hundredth is a thousandth, etc.
Add your personal information.
1. There are 12 basketball teams in a league. If each of the teams plays each of the other teams once and only once, how many games take place?
12 x 11 = 132 x 1/2 = 66 games
number of teams, number of other teams, the numerator is how many times each other, denominator is number of teams playing in one game.
2. I have four 3-cent stamps and three 7-cent stamps. Using one or more of these stamps, how many different amounts of postage can I make?
4 3-cent
3 7-cent
19 postage amounts
I wrote out all variations from the quantity of stamps and got 19.
Problem Solving
R1: 4A =5G
R2: I= 2G+A
A3: I +3G ? 4A
2G+A+3G? 4A
5G+A > 4A
1) Understanding the problem (using your own words)
2) plan to strategy
3) Implement
4) Look back, is it a reasonable answer?
George Polya
• believes in the 4 steps above
Discard the Old Books Problem
first class- 1/6
second class - 1/5
third class - 1/4
fourth class - 1/3
fifth class- 1/2
This left 14 books for the 6th period to take.
TOTAL: 84 books
There are seven people in a room. If each person shakes every other person’s hand, how many handshakes will take place? One way to solve this problem is to make a chart.
Person 1 shakes hands with: 2, 3, 4, 5, 6, and 7. 6 handshakes
Person 2 shakes hands with: 3, 4, 5, 6, and 7.
5 handshakes
Person 3 shakes hands with: 4, 5, 6, and 7.
4 handshakes
Person 4 shakes hands with: 5, 6, and 7.
3 handshakes
Person 5 shakes hands with: 6, and 7.
2 handshakes
Person 6 shakes hands with: 7.
1 handshake
Person 7 has already shaken hands with everyone.
0 handshakes
21 handshakes in total
Worked on Mind Map.
Final on Thursday.
Went over what topics are going to be on the final.
"The Chip Method"
yellow=positive
red=negative
zero pair (+)(-)
Addition
+5 + (-1) = +6
(used the chip method to show a circle with the values)
Subtraction
+5 - +2 =+3
(used the chip method to show a circle with the values)
Multiplication
+3 x +2 = +6
3 groups of positive 2
3 circles of 2
EX: -3 x +2
Since you can't have negative groups you can change the order using the commutative property.
Division
+3 x +2 = +6
+6 divided by +2 = +3 OR +6 divided by 3 = +2
